A cooled off-axis three-mirror system with a large rectangular field of view based on freeform surface is designed to satisfy the requirement of infrared remote sensing using a large plane array detector. The off-axis three-mirror system is composed of one even aspherical surface and two freeform surfaces, achieving secondary imaging with a real exit pupil that matches the cold shield, resulting in 100% cold shield efficiency. The system has larger rectangular field and decent imaging quality compared to other off-axis three-mirror systems, which ensures the adaption to large-format infrared detectors with a 4 k resolution. The system has a focal length of 150 mm, working waveband of 1.5-5 μm, F-number of 5, and field of view of 30°×25°. The primary mirror is even-order aspherical surface, and the secondary and third mirror are XY polynomial surfaces. High-order aberrations are properly corrected with the adoption of freeform surfaces, so the modulation transfer function of the system at 25 lp/mm exceeds 0.4 across all fields of view, meeting the imaging quality requirements of large-format infrared detectors. An off-axis three-mirror systems with large rectangular field of view is presented in this paper. The initial structure is a coaxial three-mirror system with its optical power distribution being convex-concave-concave (Fig.1). The curvatures of three mirrors are calculated by eliminating primary aberrations based on Seidel aberration theory. The off-axis three-mirror system is derived from the coaxial structure by shifting the field center. According to Nodal aberration theory, even aspherical surfaces are adopted to shift aberration contributions of surfaces to new field centers so they can compensate for each other (Fig.3). The off-axis three-mirror system with large field of view in tangential direction is further optimized with pupil shifting (Tab.1). The secondary and third mirror are then converted to XY polynomial surface to expand field of view in horizontal direction while the image quality is not degenerating. The optimized off-axis three-mirror system is presented (Fig.5) with primary mirror being even aspherical surface, the secondary and third mirror being XY polynomial free-form surfaces. The system meets the requirements of the detector and the design specifications (Tab.2) and the efficiency of cold diaphragm is 100%. The modulation transfer function of the system at 25 lp/mm exceeds 0.4 across all fields of view (Fig.6). RMS radius of spot diagram for all fields of view are less than Airy disk radius (Fig.7), indicating a good imaging quality. The maximum distortion of the system is -4.88%, which is acceptable and can be corrected by specific image processing algorithm. A tolerance analysis is conducted on the system, proving a good instrumentation feasibility (Fig.9). A cooled off-axis three-mirror system with a large rectangular field of view is presented in this paper. The field of view of the system is 30°×25°, and F-number is 5, ensuring the adaption to 4000×3400@20 μm infrared detector. Of three mirrors of the system, the primary mirror is even aspherical surface, and the secondary and third mirror are XY polynomial free-form surfaces. The system is a re-imaging structure with no obscuration and a real exit pupil matching cold shield of the detector, achieving 100% cold shield efficiency. The image quality is good when the system works in 1.5-5 μm waveband, thus the system has broad application in optical remote imaging and sensing field.